Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10426710 | Nonlinear Analysis: Real World Applications | 2005 | 19 Pages |
Abstract
We consider a predator-prey system with nonmonotonic functional response. The bifurcation analysis of the model shows that Hopf bifurcation can occur as the delay Ï (taken as a parameter) crosses some critical values and the system has a Bogdanov-Takens singularity for any time delay value. Following the procedure of deriving normal form given by Faria and Magalhães, we compute the normal form for the Hopf bifurcation of the model, and study the stability of the bifurcating non-trivial periodic solutions. We also obtain a versal unfolding of the model at the Bogdanov-Takens singularity under certain conditions.
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Authors
Zhihua Liu, Rong Yuan,